The initial kinetic energy of the electrons is expressed as:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{A}}}{\mathbf{+}}{{\mathbf{K}}}_{{\mathbf{B}}}}$

Two electrons, each with mass m and charge q, are released from positions very far from each other. With respect to a certain reference frame, electron A has initial nonzero speed v toward electron B in the positive x direction, and electron B has initial speed 3v toward electron A in the negative x direction. The electrons move directly toward each other along the x axis (very hard to do with real electrons). As the electrons approach each other, they slow due to their electric repulsion. This repulsion eventually pushes them away from each other. What is the minimum separation r_{min} that the electrons reach? Express your answer in term of q, m, v, and k (where k=14πϵ0)

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